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Chapter 3.5

Proving Lines Parallel. Chapter 3.5. Concept. Concept. Identify Parallel Lines. A. Given 1  3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. 1 and 3 are corresponding angles of lines a and b.

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Chapter 3.5

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  1. Proving Lines Parallel Chapter 3.5

  2. Concept

  3. Concept

  4. Identify Parallel Lines A. Given 1  3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. 1 and 3 are corresponding angles of lines a and b. Answer:Since 1  3, a║b by the Converse of the Corresponding Angles Postulate.

  5. Identify Parallel Lines B. Given m1 = 103 and m4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. 1 and 4 are alternate interior angles of lines a and c. Answer:Since 1 is not congruent to 4, line a is not parallel to line c by the Converse of the Alternate Interior Angles Theorem. Example 1

  6. A. Given 1  5, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ║ n B. Yes; m ║ n C. Yes; ℓ║ m D. It is not possible to prove any of the lines parallel.

  7. B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ║ n B. Yes; m║ n C. Yes; ℓ║ m D. It is not possible to prove any of the lines parallel.

  8. Find mZYN so that || . Show your work. Use Angle Relationships

  9. Find x so that || . A.x = 60 B.x = 9 C.x = 12 D.x = 12

  10. GAMES In the game Tic-Tac-Toe, four lines intersect to form a square with four right angles in the middle of the grid. Is it possible to prove any of the lines parallel or perpendicular? Choose the best answer. A. The two horizontal lines are parallel. B. The two vertical lines are parallel. • The vertical lines are perpendicular to the horizontal lines. • All of these statements are true.

  11. Write a proof for the following statement: If and , find the value of x to prove that line m and line n are parallel

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